Context. It has become evident that one-zone synchrotron self-Compton models are not always adequate for very high-energy (VHE) gamma-ray-emitting blazars. While two-component models perform better, they are difficult to constrain due to the large number of free parameters.
Aims. In this work, we make a first attempt at taking into account the observational constraints from very long baseline interferometry (VLBI) data, long-term light curves (radio, optical, and X-rays), and optical polarisation to limit the parameter space for a two-component model and test whether or not it can still reproduce the observed spectral energy distribution (SED) of the blazars.
Methods. We selected five TeV BL Lac objects based on the availability of VHE gamma-ray and optical polarisation data. We collected constraints for the jet parameters from VLBI observations. We evaluated the contributions of the two components to the optical flux by means of decomposition of long-term radio and optical light curves as well as modelling of the optical polarisation variability of the objects. We selected eight epochs for these five objects based on the variability observed at VHE gamma rays, for which we constructed the SEDs that we then modelled with a two-component model.
Results. We found parameter sets which can reproduce the broadband SED of the sources in the framework of two-component models considering all available observational constraints from VLBI observations. Moreover, the constraints obtained from the long-term behaviour of the sources in the lower energy bands could be used to determine the region where the emission in each band originates. Finally, we attempt to use optical polarisation data to shed new light on the behaviour of the two components in the optical band. Our observationally constrained two-component model allows explanation of the entire SED from radio to VHE with two co-located emission regions.